Heat oil in a 5- to 6-quart heavy pot over medium-high heat until it shimmers, then sauté onion with 1/2 teaspoon salt until softened, 3 to 5 minutes. Stir in garlic and sauté 1 minute, then add pasta, broccoli rabe stems, and 3/4 cup hot broth and simmer briskly, stirring constantly, until broth is absorbed. Continue simmering and adding hot broth, about 3/4 cup at a time, stirring frequently and letting each addition be absorbed before adding the next, until pasta is almost al dente and creamy-looking, 12 to 13 minutes. Stir in remaining broccoli rabe and 1/4 teaspoon pepper and cook, stirring, until pasta is al dente and broccoli rabe is just tender, 2 to 3 minutes. (If needed, add more hot broth to moisten; there will be some broth left over.) Stir in cheese and salt and pepper to taste. Serve with more cheese on the side.